PokéBase - Pokémon Q&A
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I know that Magikarp on its own has a 65% encounter rate, but I am interested in knowing what are the odds of Magikarp appearing specifically at level 15 when you reel in one with an Old Rod.

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The encounter rate of finding a level 15 Magikarp in Dewford Town when fishing with the Old Rod should be 32.5%, on the assumption that the chance of getting a level 10 or level 15 Magikarp is equal. You've got a 65% chance to encounter a Magikarp, and a 50% chance for it to be level 15. They cannot be encountered on any of the levels in between, according to Bulbapedia.

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Tfw Pokémon db dot net has incorrect info
IT DOES NOT TAKE IT BACK
It says on the page the level rage is 10-15 which makes my answer incorrect :sob:
I am pretty sure that the odds aren't even, as I have tried in the past to fish for a level 15 one and never got one within around ten encounters, which is why I am asking this question, as to know what is the exact chance.